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South East Mathematical Olympiad
2021 South East Mathematical Olympiad
7
China South East Mathematical Olympiad 2021 Grade10 P7
China South East Mathematical Olympiad 2021 Grade10 P7
Source:
July 30, 2021
inequalities
algebra
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be pairwise distinct positive real, Prove that
a
b
+
b
c
+
c
a
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
<
1
7
(
1
∣
a
−
b
∣
+
1
∣
b
−
c
∣
+
1
∣
c
−
a
∣
)
.
\dfrac{ab+bc+ca}{(a+b)(b+c)(c+a)}<\dfrac17(\dfrac{1}{|a-b|}+\dfrac{1}{|b-c|}+\dfrac{1}{|c-a|}).
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
ab
+
b
c
+
c
a
<
7
1
(
∣
a
−
b
∣
1
+
∣
b
−
c
∣
1
+
∣
c
−
a
∣
1
)
.
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